" ... there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry." Peter W. Michor.

Includes bibliographical references (pages 575-587) and index.

Print version record.

Real differentiable manifolds with corners -- The Whitney extension theorem and the inverse mapping theorem for differentiable manifolds with corners -- Submanifolds and immersions -- Submersions and quotient manifolds -- Subimmersions -- Lie groups -- Transversality -- Parametrized theorems of the density of the transversality -- Spaces of differentiable maps -- Approximation of differentiable maps -- Openness and density of the transversatility.

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